sanju09 wrote:In the x y-plane, which of the following is closest to the area of a triangle whose vertices are (√2, 0), (2, √10), and (5, 0)?
(A) 4
(B) 6
(C) 8
(D) 11
(E) 14
Any side of a triangle can be considered the base. Each base has a corresponding height. (So a triangle has three bases, and each base has a corresponding height.) To find the height that corresponds to a given base, draw a line from the vertex opposite the base so that it creates a right angle with the base.
In the problem above, one side of the triangle lies along the X axis. Let's call this side the base. The length of the base will then be the difference of the x values:
b = 5 - √2 = 5 - 1.4 = 3.6 approximately.
The corresponding height will be a line drawn from (2, √10) to the x axis so that the line and the x axis form a right angle. The length of this height will be √10.
h = √10 = 3.2 approximately.
So Area = 1/2(b)(h) = 1/2 * (3.6) * (3.2) = 5.8 approximately.
The correct answer is B.
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